In this paper, we propose an effective scheme for rapidly implementing \(\pi \) phase gate in a two-distant-atom–cavity system by combining superadiabatic scheme and quantum Zeno dynamics to construct shortcuts to adiabatic passage. As a typical application of the fast phase gates, a creation of N-atom cluster states is put forward. The influence of various decoherence processes such as atomic spontaneous emission and cavity decay on the fidelity is discussed. Numerical simulations show that the scheme is robust against decoherence caused by atomic spontaneous emission and cavity decay. In this work, superadiabatic shortcuts are used to prepare cluster states for the first time, which is faster than the traditional adiabatic passage technique.
